Use the power series 00 Tir- E(-19^x", \x| < 1 1 + x n = 0 to find a power series for the function, centered at 0. f(x) : In(x + 1) = dx x + 1 f(x) = Σ n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
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Use the power series
1
1 + x
(-1)"x", Ix| < 1
n = 0
to find a power series for the function, centered at 0.
1
dx
X + 1
f(x) = In(x + 1) =
00
f(x) = E
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
Transcribed Image Text:Use the power series 1 1 + x (-1)"x", Ix| < 1 n = 0 to find a power series for the function, centered at 0. 1 dx X + 1 f(x) = In(x + 1) = 00 f(x) = E n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
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